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Alternating-Current Circuits, Resonance and Power Transmission

Physics Grade 12 Difficulty 4/5

Beginning of the lesson

AC circuits, resonance and transmission

Alternating current reverses periodically. Resistors dissipate energy, while capacitors and inductors store and return energy, creating frequency-dependent opposition and phase shifts.

Goals: use peak and rms values; calculate reactance, impedance and phase; identify series resonance; evaluate average power and power factor; explain transformers and high-voltage transmission.

Sinusoidal quantities and rms

For v=V0 sinωt and i=I0 sin(ωt−φ), sinusoidal rms values are Vrms=V0/√2 and Irms=I0/√2. RMS values produce the same average heating in a resistor as equivalent DC. In a resistor voltage and current are in phase. For an ideal inductor current lags voltage by 90°; for an ideal capacitor current leads by 90°.

Reactance, impedance and resonance

Inductive reactance is XL=ωL; capacitive reactance is XC=1/(ωC). In a series RLC circuit, Z=√(R²+(XL−XC)²) and Irms=Vrms/Z. Resonance occurs when XL=XC, giving ω0=1/√(LC). Then impedance is minimal, current is maximal, and source voltage is in phase with current. Real components limit the response through resistance and losses.

ACLRCf₀current
Series RLC current peaks at resonance where XL=XC.

Power and transmission

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